Francis Muthaura was accused of involvement in 2007's deadly post-electoral violence in Kenya but the case has been dropped after a witness admitted lying in his incriminating testimony. Photograph: Stringer/AFP/Getty Images

International criminal court prosecutors are dropping their crimes against humanity case against a prominent Kenyan politician after a key witness admitted lying in his incriminating testimony.

The announcement is an unprecedented admission of failure by prosecutors, and the first time in the 10-year-old court's history that they have dropped a case so close to trial.

Prosecutor Fatou Bensouda told judges she was withdrawing all charges against Kenyan cabinet secretary Francis Muthaura, who is charged with crimes including murder, rape and deportation for his alleged involvement in deadly violence that erupted after his country's 2007 presidential election.

Muthaura is indicted with the Kenyan president-elect, Uhuru Kenyatta, but prosecutors argue they have more evidence against Kenyatta and his prosecution should continue.

"We do not feel that we have a reasonable prospect of conviction and therefore withdraw the charges against him," Bensouda told judges.

Muthaura, who was sitting in court, showed no emotion as Bensouda made her statement.

However, Bensouda stressed that the case against Kenyatta would continue. "This decision affects Mr Muthaura's case alone," she said.

She said witnesses in the case against Muthaura had either "been killed or have died since those events and other witnesses refuse to speak with the prosecution".

She also accused Kenyan authorities of not living up to their public pledges to fully co-operate with the court in its investigation of the violence after the 2007 vote, which left more than 1,000 people dead.

The Kenyan government "has provided only limited assistance to the prosecution and they have failed to provide the prosecution with access to witnesses or documents that may shed light on Mr Muthaura's case", said Bensouda.

She stressed that the decision was not linked to Kenya's election last week, in which Kenyatta won the presidency.

"We are all keenly aware of the most recent political developments in Kenya, but these have not … and cannot have a bearing on the decision that I make as prosecutor," Bensouda said.

Lawyers for Kenyatta are using the hearing to attempt to persuade judges to order a review of evidence that prosecutors say proves he orchestrated violence after the 2007 election.

It was not immediately clear if the withdrawal of the Muthaura case would help their cause. The lawyers say the case should be reviewed because a key prosecution witness lied, fundamentally undermining the prosecution case against him and Muthaura.

Kenyatta won last week's election despite his indictment at the Hague-based court on charges of crimes against humanity including murder, rape and deportation. Prosecutors have described him as an "indirect co-perpetrator" of violence committed by his supporters in 2007-2008.

Kenyatta, the son of Kenya's founding father, Jomo Kenyatta, and one of the country's richest men, insists he is innocent.

His trial had been scheduled to start next month, but judges last week postponed it until July, saying the defence needed more time to prepare.